Matthew,
take a look at the Emacs help topic (C-h i) for backing up files. You get there by typing 'm emacs' followed by 'm backup' in the info mode. The topic "Names: Backup Names" will tell you what to do ('m names').
Set the variable version-control to "t" in your .emacs file like so:
(setq version-control t)
This should number your backups.
/Bart